Bridging two quantum quench problems -- local joining quantum quench and M\"obius quench -- and their holographic dual descriptions

TL;DR

This paper demonstrates an equivalence between two quantum quench problems in 1+1D CFT and constructs their holographic duals, revealing new insights into their dynamics and geometric descriptions.

Contribution

It establishes a formal equivalence between local joining and M"obius quenches and derives the holographic dual of the M"obius quench from the local quench.

Findings

Equivalence relates observables between the two quench types.

Holographic dual involves a dynamic end-of-the-world brane.

Provides a geometric interpretation of the M"obius quench.

Abstract

We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the M\"obius quench, in the context of $(1+1)$-dimensional conformal field theory (CFT). Here, in the former, two initially decoupled systems (CFTs) on finite intervals are joined at $t=0$. In the latter, we consider the system that is initially prepared in the ground state of the regular homogeneous Hamiltonian on a finite interval and, after $t=0$, let it time-evolve by the so-called M\"obius Hamiltonian that is spatially inhomogeneous. The equivalence allows us to relate the time-dependent physical observables in one of these problems to those in the other. As an application of the equivalence, we construct a holographic dual of the M\"obius quench from that of the local quantum quench. The holographic geometry involves an end-of-the-world brane whose profile exhibits non-trivial dynamics.